Fallat, Shaun M. <br/><br/>
Totally nonnegative matrices / 
Shaun M. Fallat, Charles R. Johnson. 
 - Princeton :  Princeton University Press,  �2011. 
 - 1 online resource (248 pages) :  illustrations 
 - Princeton series in applied mathematics .
 - Princeton series in applied mathematics. .
<br/><br/>Includes bibliographical references (pages 219-238) and index. 
<br/><br/>Totally Nonnegative Matrices; Contents; List of Figures; Preface; Chapter 0. Introduction; Chapter 1. Preliminary Results and Discussion; Chapter 2. Bidiagonal Factorization; Chapter 3. Recognition; Chapter 4. Sign Variation of Vectors and TN Linear Transformations; Chapter 5. The Spectral Structure of TN Matrices; Chapter 6. Determinantal Inequalities for TN Matrices; Chapter 7. Row and Column Inclusion and the Distribution of Rank; Chapter 8. Hadamard Products and Powers of TN Matrices; Chapter 9. Extensions and Completions; Chapter 10. Other Related Topics on TN Matrices; Bibliography. 
<br/><br/> "Totally nonnegative matrices arise in a remarkable variety of mathematical applications. This book is a comprehensive and self-contained study of the essential theory of totally nonnegative matrices, defined by the nonnegativity of all subdeterminants. It explores methodological background, historical highlights of key ideas, and specialized topics. The book uses classical and ad hoc tools, but a unifying theme is the elementary bidiagonal factorization, which has emerged as the single most important tool for this particular class of matrices. Recent work has shown that bidiagonal factorizations may be viewed in a succinct combinatorial way, leading to many deep insights. Despite slow development, bidiagonal factorizations, along with determinants, now provide the dominant methodology for understanding total nonnegativity. The remainder of the book treats important topics, such as recognition of totally nonnegative or totally positive matrices, variation diminution, spectral properties, determinantal inequalities, Hadamard products, and completion problems associated with totally nonnegative or totally positive matrices. The book also contains sample applications, an up-to-date bibliography, a glossary of all symbols used, an index, and related references"--  ""Totally Nonnegative Matrices" is a comprehensive, modern treatment of the titled class of matrices that arise in very many ways. Methodological background is given, and elementary bidiagonal factorization is a featured tool. In addition to historical highlights and sources of interest, some of the major topics include: recognition, variation diminution, spectral structure, determinantal inequalities, Hadamard products, and completion problems"-- 
<br/><br/><br/>In English. 
<br/><br/><label>ISBN: </label>9781400839018 1400839017 
<br/><br/><label>Standard No.: </label>10.1515/9781400839018  doi 
<br/><br/><label>Source: </label>CL0500000122  Safari Books Online 22573/ctt103qx  JSTOR 9452359  IEEE 
<br/><br/><label>LCCN: </label>2010052042 
<br/><br/><label>Subjects--Topical Terms: </label><br/>Non-negative matrices.<br/>Matrices non-n�egatives.<br/>MATHEMATICS--Applied.<br/>MATHEMATICS--Matrices.<br/>MATHEMATICS--Algebra--Linear.<br/>Non-negative matrices.
<br/><br/><label>Index Terms--Genre/Form: </label><br/>Electronic books.<br/>Electronic books.
<br/><br/><label>LC Class. No.: </label>QA188  / .F35 2011eb 
<br/><br/><label>Dewey Class. No.: </label>512.9/434